Article contents
Homogeneous quasi-invariant subspaces of the fock space
Part of:
General theory of linear operators
Topological algebras, normed rings and algebras, Banach algebras
Commutative Banach algebras and commutative topological algebras
Published online by Cambridge University Press: 09 April 2009
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
In this paper, we prove that two homogeneous quasi-invariant subspaces are similar only if they are equal. Moreover, we exhibit an example to show how to determine the similarity orbits of quasi-invariant subspaces.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 75 , Issue 3 , December 2003 , pp. 399 - 408
- Copyright
- Copyright © Australian Mathematical Society 2003
References
[1]Agrawal, O., Clark, D. and Douglas, R., ‘Invariant subspaces in the polydisk’, Pacific J. Math. 121 (1986), 1–11.Google Scholar
[2]Agrawal, O. and Salinas, N., ‘Sharp kernels and canonical subspaces’, Amer J. Math. 109 (1987), 23–48.Google Scholar
[3]Ahern, P. and Clark, D., ‘Invariant subspaces and analytic continuation in several variables’, J. Math. and Mech. 19 (1970), 963–969.Google Scholar
[4]Axler, S. and Bourdon, P., ‘Finite codimensional invariant subspaces of Bergman spaces’, Trans. Amer. Math. Soc. 305 (1986), 1–13.Google Scholar
[5]Chen, X. and Douglas, R., ‘Rigidity of Hardy submodules on the unit ball’, Houston J. Math. 18 (1992), 117–125.Google Scholar
[6]Chen, X., Guo, K. and Hou, S., ‘Analytic Hilbert spaces on the complex plane’, J. Math. Anal. Appl. 268 (2002), 684–700.Google Scholar
[7]Douglas, R. and Paulsen, V., Hilbert modules over function algebra, Pitman Research Notes in Mathematics 217 (Wiley & Sons, New York, 1989).Google Scholar
[8]Douglas, R., Paulsena, V., Sah, C. and Yan, K., ‘Algebraic reduction and rigidity for Hilbert modules’, Amer. J. Math. 117 (1995), 75–92.CrossRefGoogle Scholar
[9]Guo, K., ‘Algebraic reduction for Hardy submodules over polydisk algebras’, J. Operator Theory 41 (1999), 127–138.Google Scholar
[10]Guo, K., ‘Characteristic spaces and rigidity for analytic Hilbert modules’, J. Funct. Anal. 163 (1999), 133–151.Google Scholar
[11]Guo, K., ‘Equivalence of Hardy submodules generated by polynomials’, J. Fund. Anal. 178 (2000), 343–371.Google Scholar
[12]Guo, K., ‘Podal subspaces on the unit polydisk’, Studia Math. 149 (2002), 109–120.CrossRefGoogle Scholar
[13]Guo, K. and Zheng, D., ‘Invariant subspaces, quasi-invariant subspaces and Hankel operators’, J. Funct. Anal. 187 (2001), 308–342.CrossRefGoogle Scholar
[14]Putinar, M., ‘On invariant subspaces of several variable Bergman spaces’, Pacific J. Math. 147 (1991), 355–364.CrossRefGoogle Scholar
[15]Richter, S., ‘Unitary equivalence of invariant subspaces of the Bergman and Dirichlet spaces’, Pacific J. Math. 133 (1988), 151–156.Google Scholar
[16]Rudin, W., Function theory in the unit ball of Cn (Springer, New York, 1980).CrossRefGoogle Scholar
[17]Rudin, W., New construction of functions holomorphic in the unit ball of Cn, CBMS Regional Conference Series in Mathematics 63 (Amer. Math. Soc., Providence, 1986).CrossRefGoogle Scholar
You have
Access
- 3
- Cited by